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and g(x) = x³ g(x) for all x, if gls) = 4 find 9" (5) = 4 and

and g(x) = x³ g(x) for all x, if gls) = 4 find 9" (5) = 4 and

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem Statement Given the following conditions: - \( g(5) = 4 \) - \( g'(x) = x^3 g(x) \) for all \( x \) You are required to find \( g''(5) \). **Explanation:** The problem involves calculus, specifically differentiation. The function \( g(x) \) is given, along with its first derivative in terms of \( x \) and \( g(x) \). The task is to find the second derivative at a specific point, \( x = 5 \). ### Steps to Solve 1. **Differentiate** the given expression for \( g'(x) \) to find \( g''(x) \). 2. **Substitute known values**: Use the information \( g(5) = 4 \) in your differentiated expression to find \( g''(5) \).
Transcribed Image Text:### Problem Statement Given the following conditions: - \( g(5) = 4 \) - \( g'(x) = x^3 g(x) \) for all \( x \) You are required to find \( g''(5) \). **Explanation:** The problem involves calculus, specifically differentiation. The function \( g(x) \) is given, along with its first derivative in terms of \( x \) and \( g(x) \). The task is to find the second derivative at a specific point, \( x = 5 \). ### Steps to Solve 1. **Differentiate** the given expression for \( g'(x) \) to find \( g''(x) \). 2. **Substitute known values**: Use the information \( g(5) = 4 \) in your differentiated expression to find \( g''(5) \).
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g'(x)=x3g(x)g(5)=4

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